Question about <x|P>

So we have a list of axioms.
Could someone please prove to me that these axioms dictate
P=h/i(d/dx)?
I'm interested in a proof, and if there isn't, why choosing this operator of all the operators that could keep the axioms?
Thanks!

The proof is pretty long,it can be found in any book on QM (Cohen-Tannoudji,Sakurai,...),i believe i typed it once (search for it),ain't gonna do it again.It comes naturally,yes from the axioms and from the coordinate representation of the fundamental commutation relations:
[tex] [\hat{x}_{i},\hat{p}_{j}]_{-}=i\hbar \delta_{ij} \hat{1} [/tex]

edit: Use the page numbers on the actual pages, not Adobe's page numbers.

First of all, thank you.

Now, we're getting to what's bothering me. In this doc., they simply define <p| as some kind of twisted Fourier Transform, which is what we did in our course as well.
Why? Why this? This is supposed to represent the old and familiar linear momentum.